Phaco Fundamentals Part 4: Poiseuille’s Equation

Modulating Fluid Flow: Poiseuille’s Equation

The basic equation that governs all fluid flow during phacoemulsification surgery is Poiseuille’s Equation. You already understand this equation if you’ve ever used a drinking straw to enjoy a milkshake. And the same principles even apply to setting up an irrigation system in your garden. The larger the bore of the tubing, the less resistance to flow.

Poiseuille’s Equation shows that smaller bore tubing (A) requires higher vacuum and results in a lower flow, as compared to larger bore tubing (B) which can achieve a high flow with less vacuum required. The change in flow is exponentially related to the radius of the tubing.

We are concerned with the relative relationship and not the exact values, therefore, for simplicity we can simplify this formula. The viscosity of the fluid is relatively constant, as is the length of the tubing. And the values of pi and 8 are constant. This leaves us with a simpler equation.

Flow is proportional to the change in pressure times the radius of the tubing to the fourth power. Because the value for tubing size is exponential, a small change to the radius results in a large change in the relative flow. This is clearly illustrated in a common-sense situation of drinking with straws: With a small bore straw, very high vacuum is required to achieve relatively little flow. However, with a large bore stray, low vacuum is needed to achieve good fluid flow.

Modulating Fluid Inflow

The source of fluid inflow is the bottle of balanced salt solution that is hanging on the phaco machine. The two factors that determine the rate of inflow are: the change in pressure and the radius of the inflow tubing. The change in pressure, can be modulated by raising or lowering the height of the bottle relative to the patient’s eye: the higher the bottle, the higher the infusion pressure. The inflow tubing has a large radius in order to maximize the flow and make sure that we keep our inflow greater than the outflow. Similarly, the size of the infusion channel within the phaco probe (or other infusion instrument) is kept as large as possible so as to not cause a bottleneck effect.

Modulating Fluid Outflow

For fluid outflow, there are two sources of fluid leaving the eye: (1) the fluid that is removed via the phaco probe as a result of the vacuum level generated by the fluid pump, and (2) fluid leakage from the incisions. The rate of the fluid outflow via the phaco needle is determined by the radius of the needle and tubing, as well as the change in pressure generated by the phaco machine’s fluid pump. The rate of the fluid outflow loss via the incisions depends on their size and the relative fit of the instruments within these incisions.

Some degree of fluid leakage from the incisions is helpful to allow cooling of the phaco needle and to prevent thermal injury during surgery, particularly in early in the learning stages of phacoemulsification. With the use of advanced phaco power modulations, more experienced phaco surgeons tend to move towards tighter incisions which can give more stable fluidics.

Flow Balance & Tubing Compliance

The composition, nature, and size of the inflow and outflow tubing are different, and this is important for safe and efficient phaco surgery. Surge is the situation when the outflow of fluid from the eye exceeds the inflow, even for just a fraction of a second. When this occurs, the chamber tends to collapse and the posterior capsule can be sucked into the phaco probe in an instant, resulting in a ruptured posterior capsule and vitreous loss.

In order to maintain this flow balance, where the inflow is always greater than the outflow, we can use different sized tubing. If we look at the inflow tubing we notice that it is significantly different than the outflow tubing.

Inflow vs. Outflow Tubing

The inflow tubing is large bore with walls that are thin, and the tubing is very flexible. The purpose of this tubing is to provide a high flow of fluid under low pressure situations. The maximum pressure achieved within this inflow tubing is determined by the height of the infusion bottle, and this level is not very high.

The outflow tubing is smaller bore with thick walls, and the tubing is very rigid and relatively non-compliant. Because the flow varies exponentially with the radius of the tubing, the smaller bore outflow tubing can help ensure that the outflow is less than the inflow. The outflow tubing has rigid, thick walls in order for it to have a low compliance which helps to prevent surge. The maximum pressure achieved within the outflow tubing is determined by the fluid pump of the phaco machine and can easily exceed 500 millimeters of mercury.

This high vacuum level can cause collapse of the outflow tubing if its walls are too thin and of high compliance. When the outflow tubing collapses, and then rebounds back to its normal state after the vacuum level drops, this energy release causes an immediate and dangerous surge of fluid out of the eye. This collapse of tubing due to high vacuum levels occurs most commonly during occlusion of the phaco probe, and then once the occlusion breaks, the tubing rebounds and the surge occurs. This is called post-occlusion surge and is one of the main causes of posterior capsule rupture during cataract surgery.

Phaco Needle Sizing

The size of the phaco needle is important for phaco fluidics because it affects the outflow rate. The important thing to remember from Poiseuille’s Equation is that the flow is proportional to the radius of the tube to the fourth power. This means that a small change in the size of the phaco needle can result in a very large change in the flow. Comparing two common size phaco needles, 0.9 mm versus 1.1 mm, with all other factors equal it is surprising to see that the flow through the larger 1.1 mm needle is more than twice that of the 0.9 mm needle. As the needle size decreases, the flow drops dramatically.

If we switch from a 1.1 mm phaco needle to a 0.9 mm needle, with all other phaco parameters unchanged, the relative flow will decrease by more than half – to 45% of the relative flow through the 1.1 mm needle. In order to achieve the same flow while decreasing the needle size, a very substantial increase in the pressure gradient is required. 

Once we determine the proper tubing size and phaco needle size for our needs, we can then select the other parameters of the phaco machine. Remember that the tubing size and phaco needle size are definitely variables that play an important role in the fluidics. And if you are a surgeon who also performs pars plana vitrectomy surgery, remember that there is a huge difference in fluidics and flow when comparing 20 gauge, 23 gauge, 25 gauge, and 27 gauge instrumentation.

Click below to watch a video explaining how Poiseuille’s equation determines flow:

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